S. Istrail. Constructing generalized universal traversing sequences of polynomial size for graphs with small diameter. In 31st Annual Symposium on Foundations of Computer Science, pages 439--448, St. Louis, MO, October 1990. IEEE.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... UTS s are known for various types of graphs [AAR90, BNBK 89, BRT89, HW89, Tom90] Some authors show how to construct superpolynomial length sequences [BNS89, BNBK 89, Bri87, KPS88, Nis90] and Istrail shows how to construct polynomial length sequences for certain classes of graphs [Ist88, Ist90] If one could construct polynomial length UTS s for arbitrary graphs in space O(log n) this would give an O(log n) space algorithm for ustcon, since a UTS can easily be followed in O(log n) space. Currently, though, universal traversal sequences show only that ustcon is in nonuniform O(log n) ....

S. Istrail. Constructing generalized universal traversing sequences of polynomial size for graphs with small diameter. In 31st Annual Symposium on Foundations of Computer Science, pages 439--448, St. Louis, MO, October 1990. IEEE.

....bijective labelings are the symmetric labelings, where all edges have the same label in each direction, i.e. u;v = v;u for all u; v. Universal traversal sequences for regular graphs with bijective and symmetric labelings have been considered previously by Hoory and Wigderson [32] and Istrail [35], respectively, although under different names. Both papers used the term consistent for these two different classes of restricted labelings. Not all graphs have symmetric labelings, and while every graph does have a bijective labeling, such labelings are not known to be computable in ....

S. Istrail. Constructing generalized universal traversing sequences of polynomial size for graphs with small diameter. In Proceedings 31st Annual Symposium on Foundations of Computer Science, pages 439--448, St. Louis, MO, Oct. 1990. IEEE.

....is solvable by a deterministic logarithmic space algorithm, and perhaps showing this would be an easier first step towards the main goal. In fact, considerable effort has been expended on this step, for example in studying and attempting to constructively generate universal traversal sequences [1, 2, 3, 4, 8, 9, 12, 13, 14, 15, 19, 25]. Alternatively, if deterministic and nondeterministic classes are distinct, then ustcon is a likely candidate for a problem that will separate the classes. In either case, its complexity is of interest. Settling the deterministic space complexity of ustcon is a very difficult open problem. A ....

S. Istrail. Constructing generalized universal traversing sequences of polynomial size for graphs with small diameter. In 31st Annual Symposium on Foundations of Computer Science, pages 439--448, St. Louis, MO, Oct. 1990. IEEE.

....bijective labelings are the symmetric labelings, where all edges have the same label in each direction, i.e. u;v = v;u for all u; v. Universal traversal sequences for regular graphs with bijective and symmetric labelings have been considered previously by Hoory and Wigderson [23] and Istrail [26], respectively, although under different names. Both papers used the term consistent for these two different classes of restricted labelings. Not all graphs have symmetric labelings, and while every graph does have a bijective labeling, such labelings are not known to be computable in ....

S. Istrail. Constructing generalized universal traversing sequences of polynomial size for graphs with small diameter. In 31st Annual Symposium on Foundations of Computer Science, pages 439--448, St. Louis, MO, Oct. 1990. IEEE.

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